its because i dont have the game anymore and dont own any of the consoles for the game any more, and would be quite the investment for me?
Emulator is allowed but restricted. You can find all of the rulings by clicking the rules button on the main boards and scrolling down to "Emulator Rules".
A optimal setup for running the game would be a Phat PS3, SSD and the standalone version of the game in the PS Store. The game will cost around 10 euros, the ssd around 30 euros and the console will depend where you buy it. You can find consoles from 20 euros to 80 euros, so general average is 60-100 euros in total for the setup.
However, with this setup you could play all Sly games except the PS2 version of Sly 1 optimally.
If you have any further questions I would recommend you to join the speedrunning discord. Just click the discord button right below the game name on this page.